Permutability of elements in polyadic groupoids of special form

The permutability of elements in polyadic groupoids with polyadic operation $\eta_{s,\sigma,k}$, which is determined on a $k$-th Cartesian power $A^k$ of $n$-ary groupoid $\langle A,\eta\rangle$ with the substitution $\sigma$ of the set $\{1,\dots,k\}$ and $n$-ary operation $\eta$ is studied.